In the context of TensorFlow, when dealing with recurrent neural networks, particularly MultiRNNCell, understanding the `state_size` attribute is pivotal. It informs you of the dimensionality of the state(s) that the `RNN` cell maintains and transfers between time steps during the network's operation. This article delves into the `state_size` of a `MultiRNNCell`, providing a technical breakdown and practical examples.

Understanding `state_size` in RNNs

`state_size` is an essential attribute of an `RNN` cell in TensorFlow. It essentially defines the size of the hidden state, which is a part of the cell's output used to pass information across sequence elements while processing sequential data. This attribute is critical as it influences the network’s capacity for learning temporal patterns combined with its architecture.

The Concept of MultiRNNCell

`MultiRNNCell` in TensorFlow is a composite `RNN` cell structure. It combines several `RNN` cells, such as LSTM (`tf.keras.layers.LSTMCell`) or GRU (`tf.keras.layers.GRUCell`) cells into a single entity. This stacking of cells allows for deeper representation and the ability to learn complex sequences by increasing the model's capacity.

Calculation of `state_size`

When you initialize a `MultiRNNCell`, the resulting `RNN` block behaves like a single `RNN` cell but with stacked memory within it. The `state_size` for a `MultiRNNCell` object is a tuple comprising the `state_size` of each individual `RNN` cell stacked in the MultiRNNCell.

Consider the following structure for an example in Python code:

• Each LSTM cell has two components for the secretive state: `c` (cell state) and `h` (hidden state).
• The cell state and hidden state sizes for `lstm_cell_1` are each 128, while for `lstm_cell_2`, they are each 64.
• The `MultiRNNCell` combines these into the state configuration: `((128, 128), (64, 64))`.
• Memory Capacity: Determines how much past information can be held.
• Computational Cost: More substantial states potentially require more memory and processing power.
• Learning Complexity: Larger states can capture more complex sequences but might lead to overfitting if not managed correctly.